Sieve Bomber © 2026 AEML, NTUST
WebGPU 運作中WebGPU active
不支援 WebGPU，已改用軟體繪圖No WebGPU, using software
軟體繪圖Software
底盤（<150 μm 細粉）Pan (fines)
篩網滿載！OVERLOADED
滿篩危機OVERLOAD
粒子計數視野Particle counting
即時篩分析（% 通過）Live sieve analysis (% passing)
規範Spec
完成篩分Sieved rows
列rows
細度模數 FMFineness modulus
符合級配Within spec
超出級配Out of spec
FM＝標準篩累積留篩%總和÷100（半尺寸篩不計）FM = sum of cumulative % retained on standard sieves / 100
下一批骨材Next
得分Score
顯微鏡能量Scope energy
昏倒中…Fainted…
烘乾中Drying
眼冒金星Dizzy
水洗炸彈Wet bomb
乾篩炸彈Dry bomb
準備！READY?
列篩分完成sieved!
細粉附著！Fines cling!
好痛！Ouch!
第 {n} 關Stage {n}
春・櫻花研究室Spring · Sakura Lab
夏祭・粗骨材夜市Summer Festival · Coarse Aggregate
秋紅葉・半尺寸之庭Autumn Maples · Half Sizes
冬の溫泉・濕篩修行Winter Onsen · Wet Sieving
月見之夜・顯微鏡計數Moon Night · Particle Counting
富士決戰・全粒徑分佈Mt. Fuji Finale · Full PSD
古井（ふるい）博士：「歡迎來到先進工程材料實驗室！今天要幫混凝土的細骨材做篩分析。骨材會從上方漏斗不斷掉下來，比篩孔小的顆粒會穿過篩網，比篩孔大的就被留在那一層。把同一層用正確粒徑的骨材填滿一整列，就完成篩分囉！」Dr. Furui: "Welcome to the Advanced Engineering Materials Lab! Today we run a sieve analysis on the fine aggregate. Particles finer than an opening pass through; coarser ones are retained on that sieve. Fill a whole row of a layer with the right-size particles to sieve it!"
課程重點：篩分析是最傳統的粒徑分析法，使用孔徑精確控制的 ASTM 標準篩（ASTM E11）；骨材依 ASTM C136 篩分、依 ASTM C33 判定級配。由上而下篩孔遞減：9.5 mm → 4.75 mm (No.4) → … → 150 μm (No.100)。Key idea: sieve analysis uses precisely controlled ASTM E11 sieves; aggregates are sieved by ASTM C136 and graded against ASTM C33. Openings shrink from top to bottom: 9.5 mm to 150 µm (No.100).
夏祭的煙火好漂亮！今天換粗骨材（ASTM C33 No.67）。大顆的碎石會卡在大孔篩上，要小心別讓它們堆到上一層，否則小顆粒就過不去了。Festival fireworks! Today it is coarse aggregate (ASTM C33 No.67). Big stones stop on the large sieves; do not let them pile into the layer above or the small particles cannot pass.
課程重點：粗骨材級配以 % 通過表示。樣品量要適當：太少統計性差，太多會造成篩網堵塞（blinding）。堵住的篩層要用炸彈疏通！Key idea: grading is reported as % passing. Use an appropriate sample amount: too little gives poor statistics, too much blinds the sieves. Blast clogged layers open!
紅葉的庭院裡出現了紫色虛線框的篩子――那是半尺寸篩（Half sizes）：25 mm 與 12.5 mm。它們會留住顆粒、也會畫在粒徑分佈上，但不計入細度模數。Purple dashed sieves appear among the maples: half sizes (25 mm, 12.5 mm). They retain particles and show on the PSD, but they are not counted in the fineness modulus.
課程重點：標準篩系列（Standard Series）相鄰兩篩孔徑約為 2 倍（37.5、19、9.5、4.75 mm…）；半尺寸插在其間。FM＝標準篩上累積留篩百分率總和 ÷ 100。Key idea: in the standard series each opening is about twice the next (37.5, 19, 9.5, 4.75 mm...); half sizes sit in between. FM = sum of cumulative % retained on the standard sieves / 100.
溫泉的熱氣暖呼呼～今天骨材裡混了很多細粉和團聚顆粒。乾篩時細粉會黏在粗顆粒上（白白的粉），用水洗炸彈才洗得掉，但洗完一定要烘乾！Warm onsen steam! Lots of fines and agglomerates today. In dry sieving fines cling to coarser particles (white dust); the wet bomb washes them off, but the sample must be dried afterwards!
課程重點：濕篩以水沖洗顆粒，缺點是量測後樣品必須烘乾（ASTM C325）；乾篩使用震動與敲擊裝置，缺點是細粒會附著在粗顆粒上。濕篩時也要注意不潤濕顆粒與絮凝條件。Key idea: wet sieving washes particles with water but samples must be dried afterwards (ASTM C325); dry sieving uses shaking and jarring devices, but fines can cling to coarser particles. Watch for non-wetting particles and flocculation when wet sieving.
月光下好多看不清楚的「？」骨材。集滿能量按 S 開啟粒子計數視野：用光學/電子顯微鏡看出二維等效圓直徑和落點。不過黃色「?」的讀數可能有誤差喔！Under the moon many particles show only "?". Fill the energy bar and press S for particle counting vision: microscopy reveals the 2D equivalent circular diameter and the landing spot. Yellow "?" readings may be wrong!
課程重點：粒子計數法以光學或電子顯微鏡量測數量與尺寸（二維等效圓直徑）。問題：需要大量粒子、統計顯著性通常偏低；小粒子會被大粒子遮蔽；缺乏三維資訊（厚度、體積）。Key idea: particle counting measures numbers and sizes (2D equivalent circular diameter) by microscopy. Problems: needs many particles, statistical significance is usually low, small particles are hidden by large ones, and there is no 3D information.
最終決戰！富士山下要完成從 37.5 mm 到 150 μm 的全範圍粒徑分佈，標準篩和半尺寸篩全部登場。大家合力把骨材篩乾淨吧！The finale! Below Mt. Fuji, build a full PSD from 37.5 mm to 150 µm with every standard and half-size sieve. Sieve it all together!
課程重點：完整粒徑分佈常需合併多種方法：粗粒用篩分析，次篩粒用沉降法、電阻法、雷射散射，膠體用光子相關法。不同方法依不同物理原理，同一粒子量到的粒徑很少相同，接合處常有不連續。Key idea: a full PSD often combines methods: sieves for coarse particles; sedimentation, electrical resistance or laser scattering for sub-sieve sizes; photon correlation for colloids. Different physics rarely report identical sizes, so joins are often discontinuous.
小麻糬Mochi
抹茶Matcha
柚子Yuzu
紅豆Azuki
彈珠汽水Ramune
栗子Kuri
均衡型・顯微鏡能量 +30%Balanced · +30% scope energy
烘乾快手・烘乾時間 −35%Quick dryer · drying −35%
飛毛腿・移動速度 +25%Speedy · move +25%
乾篩達人・乾篩炸彈範圍 +1Dry expert · dry range +1
水洗達人・水洗炸彈範圍 +1Wet expert · wet range +1
硬殼・不怕骨材砸、暈眩減半Tough shell · no bonk, half stun
玩家Human
電腦CPU
線上Online
你的角色Your character
已連線：{p}Connected: {p}
等待玩家加入…Waiting for a player…
對戰模式需要 2 位以上玩家Versus needs at least 2 players
還沒有線上玩家連線，要先開始嗎？（線上座位將由電腦暫代）No online player has joined yet. Start anyway? (CPU will fill online seats)
手機／平板建議按右上角「全螢幕」遊玩，並在設定開啟「螢幕搖桿」。On phones and tablets, tap Fullscreen and enable the on-screen pad in Settings.
對戰規則：每人一座篩塔，先完成 {n} 列篩分、或讓對手全部滿篩的人獲勝。你每篩完一列，對手就會掉下團聚顆粒（只有水洗才能分散）！Versus: everyone gets a sieve stack. First to sieve {n} rows, or the last stack standing, wins. Each row you sieve drops agglomerates on your rivals (only washing breaks them up)!
{p} 獲勝！{p} wins!
平手！Draw!
複習：團聚顆粒在乾篩中表現得像粗顆粒，濕篩（分散）後才會回到真正的細粒徑――所以分析前要充分分散樣品。Review: agglomerates behave like coarse particles in dry sieving; only after wet dispersion do they report their true fine size, so disperse samples well before analysis.
操作：方向鍵移動・Z (A) 吸入／吐出骨材・X (B) 放炸彈（含著骨材時為旋轉）・C 切換乾篩／水洗炸彈・V (S) 顯微鏡・P 暫停。第 2 位：WASD + G/H/J/K。Controls: arrows move · Z (A) inhale/spit · X (B) bomb (rotate while carrying) · C dry/wet bomb · V (S) microscope · P pause. Player 2: WASD + G/H/J/K.
開始篩分！Start sieving!
第 {n} 關完成！篩分析報告Stage {n} clear! Sieve analysis report
表格中「留篩量」來自你篩完的列與炸彈手動篩出的顆粒。累積留篩% 由上往下相加；% 通過＝100−累積留篩%；粒徑分佈圖為 CPFT（累積小於）對數座標，綠色帶為 ASTM C33 級配範圍。Retained amounts come from sieved rows and particles you sieved by hand with bombs. Cumulative % retained adds top-down; % passing = 100 − cumulative retained. The chart is CPFT on a log size axis; the green band is the ASTM C33 grading limit.
小測驗（答對加分）Quick quiz (bonus)
課堂小測驗 {i}／{n}Quiz {i} / {n}
答對了！+300 分、能量 +25Correct! +300 pts, +25 energy
再想想看～Not quite!
下一題Next question
前往下一關Next stage
篩網滿載了…The sieves overflowed…
骨材堆到漏斗區太久。這就是樣品量太多造成篩網堵塞（blinding）：被卡住的顆粒讓後面的細粒無法通過。記得用乾篩炸彈震開、用水洗炸彈分散細粉！Aggregate sat in the hopper zone too long. That is sieve blinding from too much sample: stuck particles block the finer ones. Shake with dry bombs and wash fines with wet bombs!
再挑戰本關Retry stage
回主選單Main menu
全關卡完成！最終報告All stages clear! Final report
恭喜成為粒徑分析大師！你已經實際操作了標準篩與半尺寸篩、乾篩與濕篩、細度模數與 CPFT，以及粒子計數法的優缺點。Congratulations, particle size master! You have worked with standard and half-size sieves, dry and wet sieving, fineness modulus and CPFT, and the pros and cons of particle counting.
玩家Player
關卡Stage
等待房主操作…（你仍可作答小測驗）Waiting for the host… (you can still answer quizzes)
篩號Sieve
留篩量Retained
留篩%% ret.
累積留篩%Cum. % ret.
通過%% passing
半尺寸half size
再來一局Rematch
自動（依場景）Auto (by scene)
節奏明快Upbeat
輕鬆慵懶Lazy chill
Pop 流行Pop
Rock 搖滾Rock
和風Japanese
熱血決戰Showdown
玩家 1（鍵盤）Player 1 (keyboard)
玩家 2（鍵盤）Player 2 (keyboard)
系統System
上Up
下Down
左Left
右Right
A 吸入／吐出A Inhale / spit
B 炸彈／旋轉B Bomb / rotate
C 切換乾篩／水洗C Dry / wet
S 顯微鏡S Microscope
暫停Pause
全螢幕Fullscreen
請按新按鍵…Press a key…
（空）(empty)
自動存檔Auto save
存檔 {n}Slot {n}
存檔Save
讀檔Load
已存到欄位 {n}Saved to slot {n}
瀏覽器空間不足，請改用匯出檔案Browser storage is full. Use Export instead.
存檔格式不正確That save file is not valid
已讀取存檔（暫停中，按繼續開始）Save loaded (paused, press Resume)
已匯出存檔檔案Save file exported
只有房主可以這樣做Only the host can do that
要重新開始本關嗎？Restart this stage?
已自動存檔，可從「讀取存檔」繼續Auto-saved. Continue from Load.
房號需為 6 碼英數字Room code must be 6 letters/digits
連線中…Connecting…
無法連上中繼伺服器，稍後重試…Cannot reach the relay, retrying…
房間 {n} 已開啟，等待玩家Room {n} open, waiting for players
已連線，等待房主…Connected, waiting for the host…
房主暫時離線The host went offline
連線中斷，重新連線中…Connection lost, reconnecting…
已加入房間，等待房主出發Joined! Waiting for the host to start
房間已滿或沒有空的線上座位Room is full or has no free online seat
已複製連結Link copied
{p} 離線，暫由電腦代打{p} left; CPU is covering
{p} 回來了！{p} is back!
{p} 加入了！{p} joined!
小提示：按 A 在漏斗附近「吸入」骨材，移動到想要的位置再按 A 吐出。骨材會穿過比它大的篩孔，停在第一層篩孔比它小的篩網上。Tip: press A near the hopper to inhale a particle, move, and press A to spit it. It falls through larger openings and stops on the first sieve finer than itself.
粗骨材大多是四格方塊，篩層只有 2 列高――含著骨材時按 B 旋轉，盡量平放！Coarse aggregate pieces are big and each sieve layer is only 2 rows tall: press B while carrying to rotate and lay them flat!
紫色虛線框是半尺寸篩。它們的留篩量會出現在粒徑分佈，但不計入細度模數。Purple dashed layers are half-size sieves: they appear in the PSD but are not counted in FM.
今天細粉很多！細粉落在骨材上會附著（白點），那一列就無法完成篩分。用水洗炸彈（按 C 切換）洗乾淨。Lots of fines today! Fines that land on particles cling (white dust) and that row cannot be sieved. Wash them with the wet bomb (press C to switch).
看不清的「？」骨材越來越多。能量滿了就按 S 開啟顯微鏡視野，看清粒徑與落點！More "?" particles now. When the energy bar is full press S for microscope vision to see sizes and landing spots!
決戰！11 層篩網全部登場，請團隊分工：有人負責吸放骨材，有人負責炸開堵塞。Finale with all 11 sieves: split the work, some place particles while others clear clogs.
半尺寸篩（½ 標記）插在標準篩系列之間；標準篩相鄰孔徑約差 2 倍。Half-size sieves (½) sit between standard sieves; standard openings differ by about 2x.
白色雲朵是 <150 μm 的細粉：若能一路落到底盤就算通過；若落在骨材上，乾篩時會附著在粗顆粒上！White puffs are fines (<150 µm). If they reach the pan they pass; if they land on particles they cling to them in dry sieving!
深色帶白點的是團聚顆粒：乾篩時表現得像粗顆粒卡在錯的篩層；用水洗炸彈分散後，就會以細粉通過。Dark speckled lumps are agglomerates: in dry sieving they act like coarse particles in the wrong layer; a wet bomb disperses them into fines.
灰色「？」是看不清粒徑的骨材。開啟顯微鏡（S）即可看出它的二維等效圓直徑。Gray "?" particles have unknown size. The microscope (S) reveals their 2D equivalent circular diameter.
有骨材停在錯誤的篩層（紅框 !）――下面被擋住、它過不去。這就是堵塞！在它旁邊放乾篩炸彈把它震開，它就會繼續往下篩。A particle stopped in the wrong layer (red !) because something blocked it: that is clogging. Place a dry bomb next to it to shake it loose so it can keep sieving down.
滿篩危機！骨材堆進漏斗區了，倒數結束前要用炸彈清出空間！Overload! Particles reached the hopper zone: clear space with bombs before the countdown ends!
這一列滿了卻沒有被篩分――因為混了錯誤粒徑、附著細粉或團聚顆粒。量測結果會失真（blinding），請清掉紅框的顆粒。This row is full but cannot be sieved: it contains wrong-size, fines-coated or agglomerated particles. Clear the red-marked ones.
篩分完成！該列骨材被記為「留在此篩上」，左側的通過% 與細度模數會即時更新。Row sieved! Those particles count as retained on that sieve; % passing and FM on the left update live.
烘乾中！濕篩後樣品必須烘乾：這段時間不能放炸彈、移動變慢，被骨材砸到會受傷！Drying! After wet sieving the sample must be dried: no bombs, slower moves, and falling particles hurt!
粒子計數視野開啟：顯示二維等效圓直徑與落點預測。但統計顯著性偏低、小粒子可能被大粒子遮住，黃色讀數可能有誤！Particle counting on: 2D equivalent diameters and landing predictions. But statistics are weak and small particles can be hidden, so yellow readings may be wrong!
細粉穿過 150 μm 篩落到底盤，記為「通過最細篩」。Fines passed the 150 µm sieve into the pan: recorded as passing the finest sieve.
細粉落在骨材上附著了（白粉）。乾篩震不掉，請用水洗炸彈。Fines clung to a particle (white dust). Shaking will not remove it: use a wet bomb.
水洗炸彈：水流會穿透顆粒、洗掉附著細粉並分散團聚顆粒，但爆炸後你得烘乾一段時間。Wet bomb: water passes through particles, washes off clinging fines and disperses agglomerates, but afterwards you must dry for a while.
乾篩炸彈：模擬震動與敲擊裝置，正確的顆粒會被篩出記錄、卡錯層的會被震鬆；但越細的顆粒越容易產生細粉附著。Dry bomb: like shaking and jarring devices. Correct particles are sieved out and stuck ones shaken loose, but finer particles often end up with fines clinging.
細粉被揚起飄走了！乾篩注意事項：細顆粒可能被帶走、灑出或揚到空氣中，造成量測損失。The fines flew away! A dry-sieving caution: fine particles can be entrained, spilled or thrown into the air, causing losses.
乾篩的副作用：細粉附著在較粗顆粒上（Fines can cling to coarser particles）。Dry sieving side effect: fines cling to coarser particles.
粒徑分佈（PSD）分析的目的是什麼？What is the purpose of a particle size distribution?
- 測定粉體的化學組成To find the chemical composition
- 得知粉體樣品中各粒徑級距的顆粒含量To find the quantity of particles in each size class
- 測定粒子的晶體結構To find the crystal structure
- 測定粉體的含水率To find the moisture content
PSD 描述的是粉體中「各粒徑級距的顆粒數量」，通常以質量或體積百分比表示。A PSD gives the quantity of particles in each size class, usually as mass or volume percentages.
「當量球徑（ESD）」的定義為何？What is the equivalent spherical diameter (ESD)?
- 粒子最長邊的長度The longest dimension of the particle
- 粒子投影面積的周長The perimeter of the projected area
- 在相同程序中行為與該粒子相同之球體的直徑The diameter of a sphere that behaves identically in the same process
- 粒子的篩孔尺寸平均值The average of the sieve openings
ESD：與「在同一程序中表現相同的球體」直徑相同，因此不同量測方法得到的 ESD 可能不同。ESD is the diameter of a sphere behaving identically in the same process, so different methods can give different ESDs.
下列何者「不是」課程中提到受粒徑分佈（堆積密度）影響的性質？Which property was NOT listed as depending on the PSD (packing density)?
- 流變Rheology
- 孔隙率與滲透性Porosity and permeability
- 乾燥收縮Drying shrinkage
- 電子能帶結構Electronic band structure
粒子堆積密度是總粒徑分佈的函數，進而影響流變、孔隙率、滲透性、乾燥收縮等。Packing density depends on the whole PSD and controls rheology, porosity, permeability and drying shrinkage.
CPFT 的意思是？What does CPFT stand for?
- Cumulative Percent Finer Than（累積小於百分率）Cumulative Percent Finer Than
- Cumulative Percent Greater Than（累積大於百分率）Cumulative Percent Greater Than
- Coarse Particle Fraction TestCoarse Particle Fraction Test
- Constant Particle Flow TechniqueConstant Particle Flow Technique
CPFT＝累積小於（某粒徑）的百分率；CPGT（累積大於）較少使用。篩分析的「% 通過」就是 CPFT。CPFT is cumulative percent finer than a size; CPGT is less common. Sieve "% passing" is a CPFT.
直方圖（頻率分佈）表示的是？A histogram (frequency distribution) shows…
- 小於某粒徑的累積百分率The cumulative percent finer
- 每個粒徑級距中顆粒的體積或質量百分比Volume or mass % of particles in each size class
- 粒子數隨時間的變化Particle number versus time
- 粒子密度與粒徑的關係Density versus size
直方圖為各級距的體積或質量百分率；累積分佈則有 CPFT 與 CPGT。Histograms give the volume or mass % in each class; cumulative distributions are CPFT and CPGT.
粒徑分佈圖的粒徑軸常用對數尺度，主要原因是？Why is a log size axis usually used for PSD plots?
- 對數尺度計算比較簡單Logs are easier to compute
- ASTM 規定只能用對數ASTM forbids linear axes
- 粒徑跨越多個數量級，對數尺度能讓所有數值容易區分Sizes span decades, so a log scale lets all values be distinguished
- 對數尺度可消除量測誤差Logs remove measurement error
線性尺度會把細顆粒擠在一起；對數尺度讓 150 μm 到 37.5 mm 都清楚可辨。On a linear axis fine sizes crowd together; a log axis separates 150 µm to 37.5 mm clearly.
ASTM E11 規範的內容是？ASTM E11 covers…
- 試驗用金屬絲網布與篩Wire cloth and sieves for testing purposes
- 混凝土骨材規範Concrete aggregates
- 水泥細度（45 μm 篩）Cement fineness by the 45 µm sieve
- 陶瓷黏土濕篩Wet sieving of whiteware clays
E11：試驗用篩；C33：混凝土骨材規範；C136：骨材篩分析；C430：45 μm 篩測水泥細度；C325：陶瓷黏土濕篩指南。E11: test sieves; C33: concrete aggregates; C136: sieve analysis of aggregates; C430: cement fineness on 45 µm; C325: wet sieving of clays.
以 45 μm（No.325）篩測定水硬性水泥細度的標準是？Which standard measures hydraulic cement fineness with the 45 µm (No.325) sieve?
- ASTM C33ASTM C33
- ASTM C136ASTM C136
- ASTM E11ASTM E11
- ASTM C430ASTM C430
ASTM C430：Fineness of Hydraulic Cement by the 45-μm (No. 325) Sieve。ASTM C430: fineness of hydraulic cement by the 45 µm (No. 325) sieve.
細度模數（FM）的計算方式為？How is the fineness modulus calculated?
- 各篩通過百分率總和 ÷ 100Sum of % passing on all sieves / 100
- 標準篩上累積留篩百分率總和 ÷ 100Sum of cumulative % retained on the standard sieves / 100
- 最大粒徑 ÷ 最小粒徑Largest size / smallest size
- 所有篩（含半尺寸）的留篩量平均Average retained on all sieves including half sizes
FM＝Σ（150 μm、300 μm、600 μm、1.18、2.36、4.75、9.5、19、37.5 mm…標準篩的累積留篩%）÷ 100；半尺寸篩不計入。FM = sum of cumulative % retained on the standard sieves (150 µm ... 37.5 mm) / 100; half sizes are excluded.
某細骨材在 4.75、2.36、1.18 mm、600、300、150 μm 的累積留篩% 為 3、15、35、60、85、97，FM＝？Cumulative % retained on 4.75, 2.36, 1.18 mm, 600, 300, 150 µm are 3, 15, 35, 60, 85, 97. FM = ?
- 1.981.98
- 3.953.95
- 2.952.95
- 0.490.49
(3+15+35+60+85+97)/100＝295/100＝2.95（9.5 mm 篩累積留篩為 0）。細骨材 FM 一般約 2.3～3.1。(3+15+35+60+85+97)/100 = 2.95 (0% retained on 9.5 mm). Fine aggregate FM is typically about 2.3 to 3.1.
標準篩系列（Standard Series）中，相鄰兩篩的孔徑比約為？In the standard sieve series, adjacent openings differ by a factor of about…
- 22
- 1.11.1
- 55
- 1010
37.5→19→9.5→4.75→2.36→1.18 mm→600→300→150 μm，每一個約為下一個的 2 倍；12.5、25 mm 等為半尺寸。37.5, 19, 9.5, 4.75, 2.36, 1.18 mm, 600, 300, 150 µm: each about twice the next; 12.5 and 25 mm are half sizes.
關於半尺寸篩（Half sizes），何者正確？Which is true about half-size sieves?
- 它們的孔徑都比 150 μm 小They are all finer than 150 µm
- 它們的累積留篩% 要加進細度模數Their cumulative % retained is added into FM
- 只能用於濕篩They are only for wet sieving
- 介於標準篩之間，用於級配規範，但不計入細度模數They sit between standard sieves, used for grading specs, but not counted in FM
粗骨材級配（如 C33 No.57）常用 25、12.5 mm 等半尺寸篩，但 FM 只計標準篩。Coarse gradings such as C33 No.57 use half sizes like 25 and 12.5 mm, but FM counts only standard sieves.
濕篩（Wet sieving）的主要缺點是？The main drawback of wet sieving is…
- 細粒會附著在粗顆粒上Fines cling to coarser particles
- 量測後樣品必須烘乾Samples must be dried after measurement
- 無法量測細顆粒It cannot measure fines
- 需要電子顯微鏡It needs an electron microscope
濕篩用水沖洗顆粒，缺點是樣品要烘乾（遊戲中：水洗炸彈後的烘乾時間）。Wet sieving washes particles with water; the sample must be dried afterwards (the drying time after a wet bomb).
乾篩（Dry sieving）的主要缺點是？The main drawback of dry sieving is…
- 細粒可能附著在較粗的顆粒上Fines can cling to coarser particles
- 樣品必須烘乾Samples must be dried
- 只能量測膠體It only measures colloids
- 需要已知折射率It needs the refractive index
乾篩使用震動與敲擊裝置，但 Fines can cling to coarser particles（遊戲中的細粉附著）。Dry sieving uses shaking and jarring devices, but fines can cling to coarser particles.
篩分析時放入「太多」樣品會造成什麼問題？Putting too much material on the sieves causes…
- 量測統計性不足Poor measurement statistics
- 樣品變得太乾The sample gets too dry
- 篩網堵塞（blinding）Blinding of the sieves
- 產生布朗運動Brownian motion
樣品量要適當：太少→統計性差；太多→篩網堵塞。遊戲中骨材堆到漏斗區就是堵塞危機。Use an appropriate amount: too little gives poor statistics, too much blinds the sieves.
乾篩過程需特別注意的事項是？During dry sieving, watch out for…
- 不潤濕顆粒與絮凝條件Non-wetting particles and flocculation
- 溶液的折射率The refractive index of the liquid
- 雷諾數必須小於 0.3Reynolds number below 0.3
- 表面濕氣與靜電、細粒被帶走或飛散Surface moisture, static charges, and fines lost or thrown into the air
乾篩：表面濕氣與靜電、細粒飛散；濕篩：不潤濕顆粒與絮凝、潑濺或滴落。Dry: surface moisture, static, fines thrown into the air. Wet: non-wetting particles, flocculation, splashing.
混凝土骨材依 ASTM C136 進行篩分析，主要採用哪種方式？ASTM C136 sieve analysis of concrete aggregates mainly uses…
- 雷射散射Laser scattering
- 乾篩（細粉含量另以 ASTM C117 水洗求得）Dry sieving (material finer than 75 µm by washing per ASTM C117)
- 沉降法Sedimentation
- 光子相關法Photon correlation
C136 以乾燥樣品機械篩分；若需 75 μm 以下含量，先依 C117 水洗再烘乾――這正是課堂「Think!」的答案。C136 sieves an oven-dried sample; material finer than 75 µm is found by washing per C117 first. That answers the "Think!" slide.
粒子計數法（Particle counting）量測的尺寸是？Particle counting reports sizes as…
- 二維等效圓直徑2D equivalent circular diameter
- 當量球徑（由沉降速度）ESD from settling velocity
- 篩孔尺寸Sieve opening
- 流體力學直徑Hydrodynamic diameter
以光學或電子顯微鏡計數數量與尺寸（2D equivalent circular diameter），適合磁性鐵氧體等特殊粉體。Optical or electron microscopy gives numbers and 2D equivalent circular diameters; good for special powders like magnetic ferrites.
粒子計數法的主要問題「不包括」下列何者？Which is NOT a major problem of particle counting?
- 統計顯著性通常偏低Statistical significance is usually low
- 小粒子可能被大粒子遮蔽Small particles may be blocked by large ones
- 樣品量測後必須烘乾Samples must be dried after measurement
- 缺乏三維（厚度、體積）資訊Lack of 3D (thickness, volume) information
「必須烘乾」是濕篩的缺點。計數法問題：需大量粒子、統計性低、非所有粒子都獨立可見、缺乏 3D 資訊。Drying is a wet-sieving drawback. Counting problems: many particles needed, low statistics, not all visible, no 3D information.
以立體學（stereology）由 2D 影像推得 3D 性質，需要什麼條件？Using stereology to get 3D properties from 2D images requires…
- 粒子必須是導電的Conductive particles
- 雷諾數小於 0.3Reynolds number below 0.3
- 粒子必須稀釋到 1 vol% 以下Dilution below 1 vol%
- 粒子方向完全隨機（片狀粒子很難做到）Total randomness of orientation (hard for platy particles)
立體學需粒子方向完全隨機，且樣品製備與計算複雜；片狀粒子容易定向排列。Stereology needs totally random orientation and complicates preparation and calculation; platy particles tend to align.
沉降法量測粒徑的原理是？Sedimentation measures size because…
- 粒子散射光的角度與粒徑有關Scattering angle depends on size
- 沉降速度是粒徑的函數（Stokes 定律）Settling velocity is a function of size (Stokes' law)
- 電阻變化與粒子體積成正比Resistance change is proportional to volume
- 布朗運動速度與粒徑有關Brownian velocity depends on size
粒子在重力下沉降，速度依 Stokes 定律與粒徑相關；適用約 300 μm～0.1 μm。Particles settle under gravity with a size-dependent Stokes velocity; range about 300 µm to 0.1 µm.
Stokes 定律用於沉降分析時的假設為？Stokes' law in sedimentation assumes…
- 粒子為球形，且彼此距離足夠、各自獨立沉降Spheres, far enough apart to settle independently
- 粒子為片狀且彼此團聚Platy, agglomerated particles
- 粒子不透光Opaque particles
- 粒子會導電Conductive particles
假設：球形、間距足夠、獨立沉降。低固含量可避免干擾，但統計性又不足――這是兩難。Assumptions: spheres, enough separation, independent settling. Low solids avoid hindrance but weaken statistics: a dilemma.
沉降粒子在不受阻礙沉降條件下，雷諾數須小於多少？For unhindered settling the Reynolds number must be below…
- 20002000
- 3030
- 0.30.3
- 0.0030.003
Re（慣性力/黏滯力）＜0.3；粗顆粒沉降太快會產生尾流，典型陶瓷粒徑上限約 75～150 μm。Re (inertial / viscous force) < 0.3. Coarse particles settle fast and make a wake; typical ceramic upper limit is about 75 to 150 µm.
為何極細顆粒（膠體，<1 μm）難以用重力沉降準確量測？Why are colloids (<1 µm) hard to measure by gravity sedimentation?
- 它們不透 X 光They block X-rays
- 它們會溶解They dissolve
- 雷諾數太大Reynolds number too high
- 布朗運動大於重力，無法預期地沉降Brownian motion exceeds gravity, so they do not settle predictably
膠體的布朗運動 > 重力，沉降不可預期；常用範圍約 1～150 μm，可用離心沉降擴展。Brownian motion > gravity for colloids; practical range about 1 to 150 µm, extended by centrifugal sedimentation.
離心沉降（Centrifugal sedimentation）的效果是？Centrifugal sedimentation…
- 提高加速力，同時降低偵測粒徑的上限與下限Raises the acceleration and lowers both the lower and upper size limits
- 只提高偵測上限Only raises the upper limit
- 讓布朗運動變大Increases Brownian motion
- 不需要已知密度Removes the need for density
加速力↑：更細的粒子也能沉降（下限↓），但粗粒子太快（上限也↓）。Higher acceleration lets finer particles settle (lower limit down) but coarse ones settle too fast (upper limit down too).
以 X 光吸收偵測沉降時，哪種粉體不適用？Which powder does not suit X-ray absorption detection in sedimentation?
- 長石粉Feldspar
- 碳粉末（對 X 光透明）Carbon powders (transparent to X-rays)
- 氧化鋁粉Alumina
- 水泥Cement
碳對 X 光幾乎透明，無法以 X 光吸收量測濃度變化。Carbon is nearly transparent to X-rays, so absorption cannot track its concentration.
雷射散射法中，大顆粒的散射特徵是？In laser scattering, large particles scatter light…
- 廣角、低強度At wide angles, low intensity
- 完全不散射Not at all
- 窄角、高強度At narrow angles, high intensity
- 只產生都卜勒頻移Only with a Doppler shift
大顆粒：窄角高強度；小顆粒：廣角低強度。量測範圍約 20 nm～2 mm。Large: narrow angle, high intensity; small: wide angle, low intensity. Range about 20 nm to 2 mm.
Fraunhofer 近似的「不當假設」是？The inappropriate assumption of the Fraunhofer approximation is…
- 粒子不透光Opaque particles
- 繞射角很小Small diffraction angles
- 需要折射率It needs the refractive index
- 散射效率與粒徑無關Scattering efficiency is independent of size
Fraunhofer 假設不透光、小角度（只適合大顆粒），且錯誤地假設散射效率與粒徑無關；Mie 理論則利用粒子與介質的折射率差。Fraunhofer assumes opaque particles and small angles (big particles only) and wrongly assumes size-independent efficiency; Mie theory uses the refractive index difference.
Mie 理論預測散射強度時需要什麼資訊？Mie theory predicts intensity from…
- 粒子與分散介質的折射率差The refractive index difference between particle and medium
- 粒子的電阻Particle resistance
- 粒子的沉降速度Settling velocity
- 篩孔尺寸Sieve openings
Mie 理論以折射率差預測強度；同一碳酸鈣樣品用 Mie 與 Fraunhofer 會得到不同分佈。Mie uses the refractive index difference; the same CaCO3 gives different PSDs with Mie and Fraunhofer.
若部分粒子超出雷射儀器偵測範圍，結果應如何呈現？If some particles are outside the detection limits, results should be…
- 正規化成 100% 後畫 CPFTNormalized to 100% as a CPFT
- 以直方圖呈現，不應正規化成 CPFTPresented as histograms, not normalized CPFT
- 改用 CPGT 即可Converted to CPGT
- 直接捨棄該樣品Discarded
範圍外的粒子量測不到；強行正規化成 100% CPFT 會失真，應以直方圖呈現。Out-of-range particles are missing, so forcing a 100% CPFT misleads; use histograms.
光子相關法（動態光散射）量測粒徑的依據是？Photon correlation (dynamic light scattering) relies on…
- 沉降速度Settling velocity
- 電阻變化Resistance change
- 膠體的布朗運動：粒子越小、運動越快，用都卜勒頻移量測Brownian motion of colloids: smaller is faster, measured by Doppler shift
- 篩網留篩量Mass retained on sieves
粒子遠離光源時散射頻率降低（都卜勒效應）。範圍約 1 nm～6 μm，涵蓋沉降法無法量測的區間。Particles moving away lower the scattered frequency (Doppler). Range about 1 nm to 6 µm, covering sizes sedimentation cannot.
背向散射（back-scattering）光子相關技術的優點是？An advantage of back-scattering photon correlation is…
- 可量測高固含量懸浮液，不需稀釋（約 40%）High-solids suspensions without dilution (~40%)
- 可量測到 2 mm 的顆粒Measures particles up to 2 mm
- 不需要雷射No laser needed
- 只量測粒子體積Measures only particle volume
背向散射可量高濃度懸浮液（樣本槽約 2 cm³、20～70 °C），但仍需結合其他方法的結果。Back-scattering handles concentrated suspensions (2 cm³ cell, 20 to 70 °C) but must be combined with other techniques.
庫爾特原理（Coulter principle）中，電阻（阻抗）變化與什麼成正比？In the Coulter principle the impedance change is proportional to…
- 粒子的表面電荷Surface charge
- 粒子的折射率Refractive index
- 粒子的沉降速度Settling velocity
- 通過小孔的粒子體積The volume of the particle traversing the orifice
粒子隨電流被吸過小孔，阻抗變化正比於粒子大小（體積）；範圍約 0.4～1200 μm。Particles drawn through an orifice with a current change the impedance in proportion to their size (volume); range about 0.4 to 1200 µm.
電阻法（電感區法）對樣品的要求是？Electrical resistance analysis requires…
- 高固含量、不需分散High solids, no dispersion
- 樣品稀釋、充分分散與解凝，粒子逐一通過小孔Diluted, well deflocculated and dispersed samples, one particle at a time
- 粒子必須不透光Opaque particles
- 粒子必須為片狀Platy particles
樣品需稀釋、分散良好，粒子必須獨立通過；約 15 分鐘，需重複以得統計顯著結果。優點：對多數材料性質不敏感。Dilute, deflocculate and disperse so particles travel independently; about 15 min and should be repeated. It is insensitive to most material properties.
合併不同方法的 PSD 時，課程建議的分工是？When combining PSDs, the suggested split is…
- 全部用雷射散射即可Laser scattering for everything
- 粗粒用光子相關，膠體用篩分Photon correlation for coarse, sieves for colloids
- 粗粒用篩分；次篩粒用沉降、電阻或光散射；膠體用光子相關Sieves for coarse; sedimentation, resistance or light scattering for sub-sieve; photon correlation for colloids
- 粗粒用沉降，細粒用篩分Sedimentation for coarse, sieves for fines
依各方法的有效粒徑範圍分工，再在重疊區接合。Assign each method to its valid size range, then join in the overlap.
為何同一粒子用不同技術量測，回報的粒徑很少相同？Why do different techniques seldom report the same size for identical particles?
- 不同技術依據不同的物理原理They are based on different physics
- 儀器都沒有校正Instruments are never calibrated
- 粒子在量測中會長大Particles grow during measurement
- 只有篩分析是正確的Only sieving is correct
篩孔、沉降速度、散射、阻抗……量的是不同的「當量尺寸」，所以合併時常出現不連續。Sieve opening, settling velocity, scattering and impedance measure different equivalent sizes, so joins are often discontinuous.
合併兩種方法的直方圖時，正確的程序是？The correct procedure for combining two histograms is…
- 直接把兩組數據相加Add the two datasets directly
- 只保留較細的方法Keep only the finer method
- 沒有重疊也可以任意接合Join anywhere even without overlap
- 在重疊區選一個粒徑級距計算細方法的倍數，再把全部數值正規化到總和 100%Pick one size class in the overlap, compute the multiplier for the finer analysis, then normalize everything to 100%
取直方圖→選重疊區單一級距→算倍數→正規化；沒有重疊就不能合併。Take histograms, choose one overlapping class, compute the multiplier, normalize; no overlap means no combination.
在本遊戲中，一個骨材穿過了 1.18 mm 篩卻停在 600 μm 篩上，它的粒徑範圍是？In the game a particle passes the 1.18 mm sieve and stops on the 600 µm sieve. Its size is…
- 大於 1.18 mmLarger than 1.18 mm
- 介於 600 μm 與 1.18 mm 之間Between 600 µm and 1.18 mm
- 小於 600 μmSmaller than 600 µm
- 小於 150 μmSmaller than 150 µm
通過上一篩（較大孔）、留在下一篩（較小孔），所以粒徑介於兩篩孔之間，記為「留在 600 μm 篩上」。It passed the coarser sieve and was retained on the finer one, so its size lies between the two openings: "retained on 600 µm".
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